### Combinations of translations

Two translations can be combined and translations can be combined with other transformations.

A translation of '4 to the right and 2 up' can be combined with a translation of '5 to the right and 3 down'.

The result is a translation of '9 to the right and 1 down'.

In algebra: $$(x, y) \rightarrow (x + 4, y + 2) \rightarrow (x + 4 + 5, y + 2 −3) \rightarrow (x + 9, y − 1)$$.